Geometry

Problems related to shapes, spaces, measurements, etc.

Problems in this category

The problem asks to find the equation of the line $AB$ given points $A(-1, 3, 2)$ and $B(2, 1, -2)$....

3D GeometryLines in 3DParametric EquationsIntersection of Lines and Planes
2025/6/15

The problem asks to find the volume of water in a rectangular parallelepiped, given its dimensions: ...

VolumeRectangular ParallelepipedUnits ConversionFractions
2025/6/15

We are given three vectors $\vec{OA} = 3\hat{i} - \hat{j}$, $\vec{OB} = \hat{j} + 2\hat{k}$, and $\v...

VectorsScalar Triple ProductParallelepipedVolumeDeterminants
2025/6/15

Given that $\angle A \cong \angle D$ and $\angle 2 \cong \angle 3$, we want to prove that $\overline...

Geometry ProofTriangle CongruenceAngle CongruenceSide CongruenceCPCTCAAS Theorem
2025/6/14

We are given that $\angle MYT \cong \angle NYT$ and $\angle MTY \cong \angle NTY$. We need to prove ...

CongruenceTrianglesAngle-Side-Angle (ASA)Side-Angle-Side (SAS)CPCTCSupplementary Angles
2025/6/14

The problem describes the transitive property of triangle congruence. Given that triangle $ABC$ is c...

Triangle CongruenceTransitive PropertyGeometric Proof
2025/6/14

The problem states that $ABCD$ is a quadrilateral. We need to prove that the sum of its interior ang...

QuadrilateralAngle SumTriangleProof
2025/6/14

The problem states that $ABCD$ is a quadrilateral. We need to prove that the sum of its interior ang...

QuadrilateralsInterior AnglesGeometric ProofsTriangles
2025/6/14

We are given triangle $PQR$ where side $PQ$ is congruent to side $RQ$, i.e., $PQ = RQ$. We need to p...

Triangle CongruenceIsosceles TriangleProofAngle BisectorSAS CongruenceCPCTC
2025/6/14

We are given that $\angle MYT \cong \angle NYT$ and $\angle MTY \cong \angle NTY$. We want to prove ...

Triangle CongruenceASA PostulateSAS PostulateCPCTCAngle BisectorRight AnglesGeometric Proof
2025/6/14